Sketch y= -(1/4)(2)^(x-4)+5 by first including a table describing its major features.
To sketch the graph of the equation y = -(1/4)(2)^(x-4) + 5, we can start by creating a table that lists some key points on the graph. From this table, we'll identify the x and y coordinates of the points.
Let's choose some values of x and find the corresponding y values to create the table:
Step 1: Choose x-values.
You can choose at least 3 or more x-values that are spread out evenly. For simplicity, let's choose the x-values -2, 0, 2, 4, and 6.
Step 2: Calculate the y-values.
Substitute each x-value into the equation y = -(1/4)(2)^(x-4) + 5 and solve for y.
When x = -2:
y = -(1/4)(2)^(-2-4) + 5
y = -(1/4)(2)^-6 + 5
y = -(1/4)(1/64) + 5
y = -(1/256) + 5
y ≈ 4.9961 (rounded to four decimals)
When x = 0:
y = -(1/4)(2)^(0-4) + 5
y = -(1/4)(2)^-4 + 5
y = -(1/4)(1/16) + 5
y = -(1/64) + 5
y ≈ 4.9844 (rounded to four decimals)
When x = 2:
y = -(1/4)(2)^(2-4) + 5
y = -(1/4)(2)^-2 + 5
y = -(1/4)(1/4) + 5
y = -(1/16) + 5
y ≈ 4.9375 (rounded to four decimals)
When x = 4:
y = -(1/4)(2)^(4-4) + 5
y = -(1/4)(2)^0 + 5
y = -(1/4)(1) + 5
y = -1/4 + 5
y ≈ 4.7500 (rounded to four decimals)
When x = 6:
y = -(1/4)(2)^(6-4) + 5
y = -(1/4)(2)^2 + 5
y = -(1/4)(4) + 5
y = -1 + 5
y = 4
Now we have our x and y coordinates:
(-2, 4.9961)
(0, 4.9844)
(2, 4.9375)
(4, 4.7500)
(6, 4.0000)
With these points, we can plot them on the graph and sketch the curve. The graph will be decreasing from left to right, starting from the leftmost point (-2, 4.9961), passing through the other points, until it reaches the rightmost point (6, 4.0000). The curve will be smooth, displaying the characteristics of exponential decay.